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A law of iterated logarithm for stationary Gaussian processes. (English) Zbl 0273.60016

MSC:
60F10 Large deviations
60F20 Zero-one laws
60G10 Stationary stochastic processes
60G17 Sample path properties
60G15 Gaussian processes
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[2] W. Feller, The general form of the so-called law of the iterated logarithm, Trans. Amer. Math. Soc. 54 (1943), 373 – 402. · Zbl 0063.08417
[3] Pramod K. Pathak and Clifford Qualls, A law of iterated logarithm for stationary Gaussian processes, Trans. Amer. Math. Soc. 181 (1973), 185 – 193. · Zbl 0273.60016
[4] James Pickands III, An iterated logarithm law for the maximum in a stationary Gaussian sequence, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 12 (1969), 344 – 353. · Zbl 0181.20703 · doi:10.1007/BF00538755 · doi.org
[5] James Pickands III, Upcrossing probabilities for stationary Gaussian processes, Trans. Amer. Math. Soc. 145 (1969), 51 – 73. · Zbl 0206.18802
[6] James Pickands III, Asymptotic properties of the maximum in a stationary Gaussian process., Trans. Amer. Math. Soc. 145 (1969), 75 – 86. · Zbl 0206.18901
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[9] C. Qualls, G. Simmons and H. Watanabe, A note on a \( 0-1\) law for stationary Gaussian processes, Mimeo Series #798, Inst. of Statistics, University of North Carolina, Raleigh, N. C., 1972.
[10] Clifford Qualls and Hisao Watanabe, Asymptotic properties of Gaussian random fields, Trans. Amer. Math. Soc. 177 (1973), 155 – 171. · Zbl 0274.60030
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[12] Antoni Zygmund, Trigonometrical series, Chelsea Publishing Co., New York, 1952. 2nd ed. · Zbl 0011.01703
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